A numerical study of relativistic fluid collapse

We investigate the dynamics of self-gravitating, spherically-symmetric distributions of fluid through numerical means. In particular, systems involving neutron star models driven far from equilibrium in the strong-field regime of general relativity are studied. Hydrostatic solutions of Einstein’s equations using a stiff, polytropic equation of state are used for the stellar models. Even though the assumption of spherical symmetry simplifies Einstein’s equations a great deal, the hydrodynamic equations of motion coupled to the time-dependent geometry still represent a set of highly-coupled, nonlinear partial differential equations that can only be solved with computational methods. Further, many of the scenarios we examine involve highly-relativistic flows that require improvements upon previously published methods to simulate. Most importantly, with techniques such as those used and developed in this thesis, there is still considerable physics to be extracted from simulations of perfect fluid collapse, even in spherical symmetry. Here our particular focus is on the physical behavior of the coupled fluid-gravitational system at the threshold of black hole formation—so-called black hole critical phenomena. To investigate such phenomena starting from conditions representing stable stars, we must drive the star far from its initial stable configuration. We use one of two different mechanisms to do this: setting the initial velocity profile of the star to be in-going, or collapsing a shell of massless scalar field onto the star. Both of these approaches give rise to a large range of dynamical scenarios that the star may follow. These scenarios have been extensively surveyed by using different initial star solutions, and by varying either the magnitude of the velocity profile or the amplitude of the scalar field pulse. In addition to illuminating the critical phenomena associated with the fluid collapse, the resulting phase diagram of possible outcomes provides an approximate picture of the stability of neutron stars to large, external perturbations that may occur in nature. Black hole threshold, or critical, solutions, occur in in two varieties: Type I and Type II. Generically, a Type I solution is either static or periodic and exhibits a finite black hole mass at threshold, whereas a Type II solution is generally either discretely or continuously self-similar and characterized by infinitesimal black hole mass at threshold. We find both types of critical behavior in our space of star solutions. The Type I critical solutions we find are perturbed equilibrium solutions with masses slightly larger than their progenitors. In contrast, the Type II solutions are continuously self-similar solutions that strongly resemble those found previously in ultra-relativistic perfect fluids. The boundary between these two types of critical solutions is also discussed.